Many binary choice multi-agent problems, where one agent may have some private information, can be modeled as 2 × $n$ bimatrix games. We show here that all 2 × $n$ bimatrix games that are full rank are strategically equivalent to rank-1 games. Given the 2 × $n$ bimatrix game, we exploit the strategic equivalence among nonzero-sum games to derive another bimatrix game, which is a rank-1 game. We then devise a new polynomial time algorithm to solve 2 × $n$ bimatrix games. We conjecture that this algorithm has comparable performance to existing polynomial time algorithms for 2 × $n$ bimatrix games, such as support enumeration. We then comment on some applications and extensions.
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机译：可以将许多二元选择多主体问题建模为2×，其中一个主体可能具有一些私人信息。
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双矩阵游戏。我们在这里显示所有2×
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从战略上讲，全等级的bimatrix游戏等同于等级1游戏。给定2×
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bimatrix博弈，我们利用非零和博弈之间的战略对等来推导另一个bimatrix博弈，即1级博弈。然后，我们设计一种新的多项式时间算法来求解2×
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双矩阵游戏。我们推测，对于2×，该算法的性能可与现有多项式时间算法相媲美。
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bimatrix游戏，例如支持枚举。然后，我们对一些应用程序和扩展进行评论。
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